The Argentine international had a torrid first season at Old Trafford, following his big-money move from Lazio, but his performances both in Europe and domestically in this campaign have won over many critics.
Veron has thanked his team-mates and Red Devils manager Sir Alex Ferguson for supporting him, and he plans to repay the faith by remaining in Manchester until 2006.
He said: "Six months ago, things were not going for me as I had hoped they would. But nowadays I am very happy and I think I will see out my contract at United, until summer 2006.
"The club, the players and the manager have all given me their support."
The 28-year-old is, though, already looking beyond his stint in The Premiership.
"I expect I will end my career back at my first club, Estudiantes," he added. "That is my wish for the not-too-distant future and I can see myself playing there in four or five years' time."
Veron is aiming to lead United to glory on home turf in this year`s Champions League final.
He added: "It is very important that the Champions League final will be held at Old Trafford.
"Being in the final is one of United's priorities. But the quarter finals will not be easy. There will be a lot of emotional pressure on us to get through."
